Decapodes are a graphical tool for the composition of physical systems.
Ultimately, this library will include tooling which takes advantage of the formalization of physical theories described by DEC provided by CombinatorialSpaces.jl.


Model predictive control (MPC) is an optimal control technique which involves solving a sequence of constrained optimization problems across a given time horizon. We present a novel Julia library that leverages our theoretical results to automate the implementation of correct-by-construction MPC problems in software.


Year Title
2024 The diagrammatic presentation of equations in categories
Kevin Arlin, James Fairbanks, Tim Hosgood, and Evan Patterson
2024 Towards a Compositional Framework for Convex Analysis
Richard Samuelson and Dario Stein
2023 A Compositional Framework for Convex Model Predictive Control
Tyler Hanks, Baike She, Matthew Hale, Evan Patterson, Matthew Klawonn, and James Fairbanks
2023 Characterizing Compositionality of LQR from the Categorical Perspective
Baike She, Tyler Hanks, James Fairbanks, and Matthew Hale
2023 Compositional Algorithms on Compositional Data: Deciding Sheaves on Presheaves
Ernst Althaus, Benjamin Merlin Bumpus, James Fairbanks, and Daniel Rosiak
2023 A compositional account of motifs, mechanisms, and dynamics in biochemical regulatory networks
Rebekah Aduddell, James Fairbanks, Amit Kumar, Pablo Ocal, Evan Patterson, and Brandon Shapiro

Journal Papers

Year Title
2023 Computational category-theoretic rewriting
Kristopher Brown, Evan Patterson, Tyler Hanks, and James Fairbanks
Journal of Logical and Algebraic Methods in Programming
2023 The application of applied category theory to quantify mission success
Robert K Garrett, James Fairbanks, Margaret Loper, and James Moreland
2022 An algebraic framework for structured epidemic modelling
Sophie Libkind, Andrew Baas, Micah Halter, Evan Patterson, and James Fairbanks
Philosophical Transactions of the Royal Society A
2022 A diagrammatic view of differential equations in physics
Evan Patterson, Andrew Baas, Timothy Hosgood, and James Fairbanks
Mathematics in Engineering
2021 Categorical Data Structures for Technical Computing
Evan Patterson, Owen Lynch, and James Fairbanks
2021 Category-Theoretic Formulation of the Model-Based Systems Architecting Cognitive-Computational Cycle
Yaniv Mordecai, James Fairbanks, and Edward Crawley
Applied Sciences

Conference Papers

Year Title
2023 A Categorical Representation Language and Computational System for Knowledge-Based Robotic Task Planning
Angeline Aguinaldo, Evan Patterson, James Fairbanks, William Regli, and Jaime Ruiz
2023 AAAI Fall Symposium on Unifying Representations for Robot Application Development
2022 Compositional Exploration of Combinatorial Scientific Models
Kristopher Brown, Tyler Hanks, and James Fairbanks
5th International Conference on Applied Category Theory
2022 Computational Category-Theoretic Rewriting
Kristopher Brown, Evan Patterson, Tyler Hanks, and James Fairbanks
15th International Conference on Graph Transformation
2021 Operadic Modeling of Dynamical Systems: Mathematics and Computation
Sophie Libkind, Andrew Baas, Evan Patterson, and James Fairbanks
4th International Conference on Applied Category Theory